In most cases as long as the Luteal Phase is not shorter than 10 days, it won't affect your ability to conceive. The worst it can do is to cause miscalculation.
For example, if you have a 30-day cycle, the instruction will tell you to start testing on day 12 (30/2-3=12). This is based on the assumption that you have a standard LP, which is half length of your entire cycle. You suppose to expect ovulation on day 15. However if you have a short LP, lets say 12 days instead of 15 days. You will not O till day 18. So you may get a tad anxious or even stop testing after day 16, wondering why you can't detect a LH surge, if there is something wrong with your ovulation. In fact your ovulation is yet to come in a couple of days time.
The easy fix is to keep testing until a surge is detected or the next period is here. Don't stop half way just because you assume you should have O'd by now then torture yourself with all those negative tests.
Knowing your own LP length will allow you to adjust the testing period accordingly. Less stressful for you.
If you suspect your LP is less than 10 days, I think you need to discuss this with your GP.
The implantation of an impregnated egg usually happens around 9DPO (some say between 8-12DPO), if your LP is shorter than 10DPO, chances are before the egg can firmly implant itself on the lining of uterus, the lining will start to peel off and the egg gone with the period blood. Situations like this, it is not that you can't conceive, indeed you can, but your body doesn't allow the baby to survive. You suffer a miscarriage before you even know it.
There are medications out there to help lengthening the Luteal Phase.